Ah bloody hell! There is a way to make social group messages private.

The forum admin has to enable this option:
Allow Join-to-View Groups

When set, this allows the creator of a group the option to only show contents (messages, pictures) of the group to members of that group (or Administrators and Moderators).
I just enabled it.

I still like private forums better, because of the richer software feature set. But, Social Groups are easier to set up.

I suppose each have a place, but damn... there is a lot of overlap.